Question

16)
The height of a triangle as 7 cm less than its
base. And its area is 9 sq. cm. find the
height and base of the triangle.​

Answer 1

Answer:

height and base of the triangle are 2 cm and 9 cm  respectively

Step-by-step explanation

let length of the base is x cm

length of height is (x-7) cm

Area of the triangle is A = 9 sq.cm

$A =\frac{1}{2} bh\\9= \frac{1}{2} \times x \times (x-7)\\18=x^2-7x\\x^2-7x-18 =0$

by factorizing and solving

$x^2 +2x-9x-18=0\\x(x+2)-9(x+2)=0\\(x+2) (x-9 )= 0\\x+2 =0 or x-9 = 0\\x=-2 OR x =9$

We can take x=9  as base of the triangle and height of the triangle is 9-7 =2 cm

Therefore height = 2 cm and base of the triangle is 9 cm