The length of hypotenuse of a right-angled triangle exceeds the length of the base by 2cm and exceeds twice

Question

The length of hypotenuse of a right-angled triangle exceeds the length of the base by 2cm and exceeds twice

The length of hypotenuse of a right-angled triangle exceeds the length of the base by 2cm and exceeds twice the length of the altitude by 1cm. Find the length of each side of the triangle and find the area of the triangle..

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Let the length of altitude be x cm.
Length of hypotenuse = 2x+ 1cm.
Length of base = 2x- 1
Now,
x² + (2x- 1) ² = (2x+ 1)²
x² = (2x+1)² - (2x-1)²
x² = 8x
x² - 8x = 0
x = 8 (Side can't be zero)
Altitude = 8cm
Base = 2(8) - 1= 15cm.
Hypotenuse = 2(8)+ 1 = 17cm.
Hence altitude is 8cm, base is 15cm, hypotenuse is 17cm.
Area of triangle = 1/2 × 8 × 15 = 60cm².