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evablogger [386]
3 years ago
10

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 .

Mathematics
2 answers:
Digiron [165]3 years ago
3 0

Answer:

Ratio of area of triangles MNP and ABC is 1.05

Step-by-step 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\times 10

Area of triangle ABC = 160\times k ,

where k is a constant.

So area of triangle MNP ∝ 7 \times 24

Area of triangle MNP = 168\times k

So ratio of area of triangles = \frac{Area of MNP}{Area of ABC}

                                              = \frac{168}{160}

                                               = 1.05

dolphi86 [110]3 years ago
3 0

Answer:

21 : 20

Step-by-step 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

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