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Chapter 11: Q30. (page 432)

An isosceles triangle has sides that are5cm,5cmand8cmlong. Find its area and the lengths of the three altitudes.

Short Answer

Expert verified

The area of triangle is12鈥夆赌�sq.鈥夆赌�unit and the length of altitudes are 3,4.8,4.8

Step by step solution

01

Step 1. Draw the diagram.

02

Step 2. Concept used.

We can use Pythagorean Theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

52=42+h2h2=25鈭�16h2=9h=3

03

Step 3. Use the concept of area of triangle.

Area of 鈻�ABCcan be found using the formula

b=BC=8h=3A=12bhA=12(8)(3)A=12鈥夆赌�sq.鈥夆赌�unit

04

Step 4. Find the altitudes.

The length of altitudeBE

b=5h=?A=12A=12bh12=12(5)(h)24=5hh=245h=4.8

Similarly, The length of altitudeCF is4.8

Therefore, the Area is12鈥夆赌�sq.鈥夆赌�unit

The length of altitudes are3,4.8,4.8.

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Most popular questions from this chapter

Find the area of each figure:

An isosceles triangle with base10and Perimeter 36 .

Find the area of each figure:

Find the area of each figure:

A rhombus with a120鈭�angle and sides 6cm

a. Use the diagram at the right. Find the area of鈻�PQRS.

b. Use the diagram at the right. Find the area of鈻�PSR.

c. Use the diagram at the right. Find the area of鈻�OSR. (Hint: Refer to鈻�PSR and use Exercise28).

d. Use the diagram at the right. What is the area of鈻�PSO?

e. Use the diagram at the right. What must the area of鈻�POQbe? Why? What must the area of鈻�OQR be?

f. Use the diagram at the right. State what you have shown in parts (a)-(e) about how the diagonals of a parallelogram divide the parallelogram.

Find the area of each figure:
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