Question

in triangle abc angle a =90, AB =14cm AC =48cm. Find the area of triangle and lenght of perpendicular from A to BC

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The area of ΔABC is 33 cm² and the length of the perpendicular dropped from A to BC is 13.44 cm.

Given

In ΔABC:-

• ∠A = 90°
• AB =14cm
• AC

To Find

1. Area of ΔABC
2. Length of the perpendicular from A to BC

Solution

∠A = 90°

Therefore ΔABC is a right triangle.

Area of a right-angled triangle= 1/2 X Base X Height

= 1/2 X 14 X 48 cm²

=336 cm².

The side opposite to the right angle i.e BC is the hypotenuse.

According to Pythagoras Theorem,

hypotenuse² = base² + perpendicular²

Therefore, length of BC = √(14² + 48²)

=√(196 +2304) cm

=√2500 cm

=50 cm

Now let the perpendicular drop be AD.

Since this too is a perpendicular ΔADB and ΔADC are right triangles as well.

Area of ΔABC = Area of ΔADB + Area of ΔADC

or, 1/2 X ADXBD + 1/2ADXCD = 336

or, 1/2AD(BD + CD) = 336

or, AD(BC) = 2X336

or, AD= 672/50

= 13.44 cm

Therefore the area of ΔABC is 33 cm² and the length of the perpendicular dropped from A to BC is 13.44 cm.

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