Question

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

Answer 1

We know that,
Area Of Triangle = 0.5 x (Base) x (Height)                 (Here, I have taken 1/2 as 0.5)
Let the base be 4k and height be 5k ( ∵ Ratio is 4:5)

Then,
Area = 0.5 x 4k x 5k
90 = 10k²
k² = 9
k= +3 or -3
Since the -3 case is not possible, we've
k=3 m

∴ Base = 4k = 4 x 3 = 12 m
and Height = 5k = 5 x 3 = 15 m

Answer 2

let the ratio of base to height be 4x:5x
area=90sq m
1/2×base×height=90
1/2×4x×5x=90
20x^2=180
x^2=180/20
x^2=9
x=3
base=4x=4×3=12m
height=5x=5×3=15m
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