Question

For the triangles ABC and MNP m∠A = m∠M, AB = 16, AC = 10, MN = 7, MP = 24. Find the ratio of the A△MNP and A△ABC .

Answer 1

21 : 20

Explanation:

Area of ABC

½ × AB × AC sinA

½ × 16 × 10 sinA

80sinA

Area of MNP

½ × MN × MP sinM

sinM = sinA because angle M = angle A

½ × 7 × 24 sinA

84sinA

Ratio:

MNP : ABC

84sinA : 80sinA

21 : 20

Answer 2

Ratio of area of triangles MNP and ABC is 1.05

Explanation:

There are 2 triangles ABC and MNP.

We are given that ,m∠A = m∠M.

AB = 16 and AC = 10.

MN = 7 and MP = 24.

Area of a triangle ∝ Product of any two sides.

So area of triangle ABC ∝ 16
`* 10`

Area of triangle ABC = 160
`* k` ,

where k is a constant.

So area of triangle MNP ∝ 7
`* 24`

Area of triangle MNP = 168
`* k`

So ratio of area of triangles =
`(Area of MNP)/(Area of ABC)`

=
`(168)/(160)`

= 1.05