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PolarNik [594]
3 years ago
9

Two triangles have bases with lengths 5in and 8in.

Mathematics
1 answer:
Elis [28]3 years ago
7 0

Answer:

i. The ratio of the areas of the two triangles is 5:8.

ii. The area of the larger triangle is 24 in².

Step-by-step explanation:

Let the area of the smaller triangle be represented by A_{1}, and that of the larger triangle by A_{2}.

Area of a triangle = \frac{1}{2} x b x h

Where; b is its base and h the height.

Thus,

a. The ratio of the area of the two triangles is:

\frac{area of the smaller triangle}{area of the larger triangle}

Area of smaller triangle = \frac{1}{2} x b x h

                                       = \frac{1}{2} x 5 x h

                                       = \frac{5}{2}h

Area of the lager triangle = \frac{1}{2} x b x h

                                           = \frac{1}{2} x 8 x h

                                           = 4h

So that;

Ratio = \frac{\frac{5}{2}h }{4h}

         = \frac{5}{8}

The ratio of the areas of the two triangles is 5:8.

b. If the area of the smaller triangle is 15 in², then the area of the larger triangle can be determined as;

\frac{area of the smaller triangle}{area of the larger triangle} = \frac{5}{8}

\frac{15}{A_{2} } = \frac{5}{8}

5 A_{2} = 15 x 8

       = 120

A_{2} = \frac{120}{5}

    = 24

The area of the larger triangle is 24 in².

         

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