Question

find the ration of the area of triangle's abc and cea , if the ratio of sides bc:ce =1:4
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Answer 1

Answer:

the ratio of the areas of the triangles is 1:4

Step-by-step explanation:

We know that for two similar triangles if the ratio of the area is square of the ratio of the sides

Given that

ratio of side BC and CE is 1:4

or, \frac{BC}{CE}=\frac{1}{4}

CE

BC

=

4

1

If the height of the triangle from A is h, then

Ratio of the areas of the triangles

\frac{\text{ar}(\triangle ABC)}{\text{ar}(\triangle CEA)}=\frac{1/2\times h\times BC}{1/2\times h\times CE}[tex] [tex]\implies \frac{\text{ar}(\triangle ABC)}{\text{ar}(\triangle CEA)}=\frac{BC}{CE}=\frac{1}{4}

ar(△CEA)

ar(△ABC)

=

1/2×h×CE

1/2×h×BC

[tex][tex]⟹

ar(△CEA)

ar(△ABC)

=

CE

BC

=

4

1

Therefore, the ratio of the areas of the triangles is 1:4