Correct option is C
Given:
△ ABC, DE ∥ BC. BC = 8 cm, DE = 6 cm
ar. △ ADE = 90 cm²
Concept Used:
If two triangle are similar, than ratio of their areas are equal to the ratio of square of their respective sides.
Solution:
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Question
In the given △ ABC, DE ∥ BC. If BC = 8 cm ,DE = 6 cm and area of △ ADE = 90 cm² , then what is the area of △ABC (in cm²) ?
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- 1)
In △ABC, AB = AC = 12 cm, BC = 5 cm and D is a point on AC such that DB = BC. What is the measure of CD?
- 2)
A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. A second right-angled triangle is similar to the first, and its hypotenuse is 39 cm. What is the area of the second triangle?
- 3)
In a quadrilateral ABCD, a line segment BD is a diagonal such that AB=CD and ∠ABD=∠CDB. Are the triangles ABD and CDB congruent? If so, by what rule?
- 4)
In a trapezoid ABCD with AB parallel to CD, the diagonals AC and BD intersect at E. What is the ratio of the area of △ABE to the area of △CDE?
- 5)
A right triangle ABC is inscribed in a circle with a diameter of 10 cm. An altitude BD is drawn from the vertex B to the hypotenuse AC. If the length of the leg AB is 6 cm, what is the length of the segment AD?
- 6)
Two right-angled triangular blocks, ABC and DEF, have ∠B = ∠E = 90°. If the lengths of the hypotenuses AC and DF are equal, and the sides AB and DE are equal, are the triangles congruent? If so, by what rule?
- 7)
In a triangle ABC, medians AD and BE intersect at G. If the length of median AD is 12 cm, what is the length of the segment AG?
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In triangle ABC, medians AD, BE, and CF intersect at the centroid G. What is the ratio of the area of triangle GAB to the area of triangle ABC?
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In ∆ABC, a line segment DE is parallel to BC, with D on AB and E on AC. If the ratio of the area of △ADE to the area of the trapezoid DECB is 4 : 21, what is the ratio of AD to DB?
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In △ABC, BD ⟂ AC at D and ∠DBC = 25°. E is a point on BC such that ∠CAE = 80°. What is the measure of ∠AEB?
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