Question

The ratio of the area of a triangle to the area of a rectangle is 3:5.The difference in their areas is 54 square inches what is the height of the triangle if its base is 2 times its height?

Answer 1

Answer:

$\sqrt{135}$

Step-by-step explanation:

Let 3x be the area of triangle and 5x be the area of rectangle

the difference between their area is= 54

therefore we can say that ●5x-54=3x

● 5x-3x=54

●2x=54

●x=27

area of triangle=3x=3×27=81 area of rectangle=5x=5×27=135

now given: height of triangle=x

base of triangle=2x

Area of triangle=1/2×Base×height=135

●1/2 × 2x × x=135

●x × x = 135

x=root 135

therefore height=

$\sqrt{135}$

Answer 2

Answer:

Step-by-step explanation:

Let 3x be the area of triangle and 5x be the area of rectangle

therefore we can say that 5x-54=3x

5x-3x=54

2x=54

x=27

area of triangle=3x=3×27=81 area of rectangle=5x=5×27=135

base of triangle=2x

=1/2×Base×height=135

1/2 × 2x × x=135

x × x = 135

x=root 135

therefore height= root 135