Question

If base of a right angled triangle is twice the base of another right angled triangle and height of the first right angled triangle is one-fourth of the other’s height, then find the ratio of areas of first triangle to second triangle.

Answer 1

Here is your answer:

Let the base of first triangle=b

The base of second triangle=2b

The height of first triangle=h

The height of second triangle=h/4

Then the ratio of first triangle to second triangle is in the attachment

Answer 2

Answer:

The ratio of areas of the first triangle to the second triangle = 1:2

Step-by-step explanation:

Given,

The base of a right angles triangle is twice the base of another

The height of the first right-angled triangle is one-fourth of the other's height

To find,

The ratio of the area of the first triangle to the second

Solution:

Recall the formula

Area of a right-angled triangle = $\frac{1}{2}$×base×height

Let 'b' be the base and 'h' be the height of the first triangle

Since the base of the first triangle is twice the base of the other we have,

The base of the first triangle = 2×base of the second triangle

b = 2×base of the second triangle

The base of the second triangle = $\frac{b}{2}$ ---------------------(1)

Again, since the height of the first right-angled triangle is one-fourth of the other’s height we have

Height of the first triangle = $\frac{1}{4}$×height of the second triangle

h =  $\frac{1}{4}$×height of the second triangle

Height of the second triangle = 4h -----------------(2)

Area of the first triangle = $\frac{1}{2}$×base×height =  $\frac{1}{2}bh$, since b is the base and h is the height of the first triangle

∴Area of the first triangle = $\frac{1}{2}bh$ ---------------(3)

Area of the second triangle = $\frac{1}{2}$×base×height

=  $\frac{1}{2} X\frac{b}{2}X4h$ (substituting the value of base and height from equations (1) and (2))

= bh

∴Area of the second triangle =bh ---------------(4)

The ratio of the areas of the first triangle to the second = $\frac{1}{2}bh$: bh

= $\frac{1}{2}:1$

= 1:2

The ratio of areas of the first triangle to second triangle = 1:2

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