Question

the base and height of a triangle are in the ratio 4:5. if the area of the triangle is 90° m^2 , find the measures of its base and height?

Answer 1

We know that area of right triangle is
$1 \div 2 \times base \times height$
Let the sides be in the ratio
$4x \: 5x$
Then the area would be
$1 \div 2 \times 4x \times 5x \: = 90 {m}^{2}$
$2x \times 5x = 90$
$10 {x}^{2} \: = 90 \\ 90 \div 10 = {x}^{2} \\ 9 = {x }^{2} \\ 3 = x$

So the sides are 12 m and 15 m

Answer 2

base=12m
height=15m
let base be 4a and height be 5a
Area of triangle = 1/2*base*height
= 1/2*4a*5a
= 10*a^2
ATQ, Area of triangle = 90 m^2
10*a^2 = 90
a^2 = 90/10 m^2
a^2 = 9 m^2
a = 3m
base = 4*a = 4*3m = 12m
height = 5*a = 5*3m = 15m