Question

area of right angled triangle is 165m square determine it's base and altitude if the later exceeds the former by 7 meter.

Answer 1

a=165m^2
let base=x
then altitude=7x
= 1/2×7x×x=165
7x^2=330
x^2=330/7
x=
$\sqrt{330 \div 7}$

Answer 2

SOLUTION :  

Let the base of a ∆  be x m, then the altitude be (x + 7) m.

Area of a ∆ = 1/2 x Base x Altitude

1/2 x  (x + 7) = 165

x (x + 7) = 165 × 2

x² + 7x = 330

x² + 7x - 330 = 0

x² + 22x – 15x – 330 = 0

[By middle term splitting]

x(x + 22) – 15(x + 22) = 0

(x + 22)(x – 15) = 0

(x + 22)  or (x – 15) = 0

x = - 22 or x = 15

Since, side can’t be negative, so x ≠ - 22 , Therefore x = 15 m

Base = x = 15 m

Altitude = x + 7 = 15 + 7 = 22 m

Hence, the base of a ∆  is 15 m and the altitude is 22 m.

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