Two sides of a right triangle measure 15 cm and 17 cm. Which of the following statements can be true of the length of the third side of the triangle A. It is between 4 cm and 7 cm. B. It is between 20 cm and 23 cm C. It is less than 10 cm.?

A and C only
B and C only
B only
A and B only

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 2 : B and C only

Concept:

Pythagoras' Theorem: The square of the hypotenuse of the right angle triangle is equal to the sum of squares of the other two sides.
(Hypotenuse)² = (Base)² + (Height)²
The hypotenuse is always the biggest side in triangle opposite to 90°

Calculation:

Given the two sides of the triangle are 15 cm and 17 cm

Here, it is not given which side is hypotenuse or the other sides so,

we have two cases CASE-1

Let the missing side be hypotenuse,

[ alt="F2 5f20127c997d750d13e7163a Prabhat.S 10-09-20 Savita D1" src="//storage.googleapis.com/tb-img/production/20/09/F2_5f20127c997d750d13e7163a_Prabhat.S_10-09-20_Savita_D1.png" style="width: 229px; height: 159px;">

⇒ x² = 15² + 17² = 225 + 289 = 514

⇒ x = √ 514 = between 22 to 23 cm

We have CASE-2

Let the other side is missing

[ alt="F2 5f20127c997d750d13e7163a Prabhat.S 10-09-20 Savita D2" src="//storage.googleapis.com/tb-img/production/20/09/F2_5f20127c997d750d13e7163a_Prabhat.S_10-09-20_Savita_D2.png" style="height: 159px; width: 229px;">

⇒ (17)² = (15)² + x²

⇒ x² = 17²- 15² = 289 - 225 = 64

⇒ x = √ 64 = 8 cm

∴ Option 2 is correct

4 views Answered 2022-09-04 04:29

Related Questions

Inside a right-angled triangle, a circle is drawn which touches all the three sides of the triangle. If the two sides of the triangle other than hypotenuse are 5 cm and 12 cm then find the radius of the circle drawn?

1 Answers 8 Views

Which of the following statements is/are true A: If the length of a cuboid is ‘x’ and its breadth and height are respectively (1/2) and (1/3) of its length, then the ratio of its surface is and its volume will be 12: x. B: If main diagonal of a cube becomes half, then the side of cube will also become half. C: If breadth of a cuboid is half of its length and it is cut into two equal pieces along the axes perpendicular to its length, then the 2 pieces formed will be cubes.?

1 Answers 4 Views

Which of the following statements is/are true A: If the sides of an equilateral triangle becomes 2√2 times, then its area will become 4√6 times. B: If the distance between any two parallel sides of a rhombus is 25% less than its diagonal, then its other diagonal will be 50% more than its side. C: If ratio between altitude and base of a right-angled triangle is 3: 5, then the ratio between its hypotenuse and base will be √30: 5.?

1 Answers 4 Views

Which of the following statements is/are true A: If two tangents, PA and PB, are formed on a circle from a point ‘P’ and OA and OB are the radius of the circle, then OAPB will be a cyclic quadrilateral. B: In a ΔABC, an incircle is formed with centre ‘O’. Then ∠BAC will be 180° less than the double of the angle made by side BC at the centre of the circle. C: The length of two tangents from a point, outside the circle, are always equal.?

1 Answers 9 Views

Which of the following statements is/are true A: The incircle of a triangle touches each side of the triangle at mid-point. B: ABCD is quadrilateral. If A, B and C are on the circumference of a circle, D is the center of the circle and AB and BC are smaller than radius of circle, then ∠ABC will be (180 – smaller ∠ADC/2). C: Angle made by a tangent on any chord of a circle will never be right angle.?

1 Answers 4 Views

Which of the following statements is/are true A: If the ratio of length and breadth of a rectangle is 4 : 3 and the side of a square is equal to length of the rectangle, then the ratio of the areas of square and rectangle will be 4 : 3. B: From each corner of a rectangular sheet, if four squares of equal side are cut, then perimeter of the rectangular sheet will be decreased. C: The diagonals of a parallelogram can never perpendicular to each other.?

1 Answers 8 Views

Consider the statements given below- A: Two triangles with same perimeter are always congruent to each other. B: In an acute angle triangle at max two angles must be less than 90°. C: Sides opposite to equal angles of two different triangles (non-congruent) will never be equal. Which of the above statement(s) is/are TRUE?

1 Answers 4 Views

A circle of maximum area is inscribed in the square. An equilateral triangle is inscribed in that circle and all the vertices of the triangle touch the circle. A triangle is formed by the joining of the midpoint of the sides of the equilateral triangle. Find the ratio of the area of the square and area of the triangle which is formed by midpoints.?

1 Answers 4 Views

Consider the following statements 1. The focal length of the eyepiece is larger than the focal length of the objective. 2. The focal length of the eyepiece is smaller than the focal length of the objective. 3. The aperture of the eyepiece lens is larger than the objective lens. Which of the following statements is/are INCORRECT about a compound microscope?

1 Answers 4 Views

A part of the sentence may or may not have an error. Find out which part has an error and mark that part as your answer. If there are no errors, mark 'No error' as your answer. The functional sections of the brain are also categorized by side-the right side and the (A)/left side, each side are responsible for different functions,(B)/ and general patterns of dysfunction may occur depending on the side of the brain sustaining an injury.(C)/ No Error (D)?

1 Answers 4 Views

এক্সাম দিয়ে মেধা যাচাই করুন

Job Preparation (1125)

Admission (754)

এসএসসি (10)

এইচএসসি (5)