Question

The sides of a right-angled triangle are p, p+1 and 5. Find the area of triangle, if the longest side measures 5 cm.

• A. 6 cm²
• B. 10 cm²
• C. 8 cm²
• D. 15 cm²

Answer 1

The correct option is A

6 cm²

p${}^2$ + (p+1)${}^2$ = 5${}^2$ (Pythagoras' Theorem)

p${}^2$ + p${}^2$ + 2p + 1 = 25

=$>$ p${}^2$ + p${}^2$ + 2p - 24 = 0

2p${}^2$ + 2p - 24 = 0

p${}^2$ + p - 12 = 0

(p - 3)(p + 4) = 0 (p + 4) = 0 or (p - 3) = 0 p = -4 or p = 3 p = 3

Area = 1/2 $\times$ 3 $\times$ 4 = 6cm${}^2$