Question

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Answer 1

Step-by-step explanation:

ABC be the given isosceles right triangle such that <B = 90° , side AC is the hypotenuse; and, AB= BC

Then, (AB)^2 + (BC)^2 = (AC)^2…. Pythagoras theorem.

(AC)^2 = 98 sq. cm. ( given)

So, (AB)^2 + ((BC)^2 = 98

But, AB = BC = a ( say) …. ( given)

Therefore, a^2 + a^2 = 98

Or, 2a^2 = 98.

So, a^2 = 98 / 2 = 49

Hence, a = AB = BC = √49 = 7 cm.

The side AC ( the hypotenuse) = √98 = √(7 *7*2)

= 7 *√2 = 7* 1.414 = 9..898cm., say, 9.9 cm.

Hence, the three sides of the right isosceles triangle are 7 cm, 7cm and ~ 9.9 cm. Answer

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Answer 2

Answer:

2) In an isoscles triangle, 2 sides are congruent.

Missing sides = x

In a right △,

Hypotenuse ² = Base² + Altitude ²

98 = x² + x²

98 = 2x²

98/2 = x²

49 = x²

√49 = x

7 = x

=》Length of the congruent sides = 7 cm

3) Using pythagorean property,

Hypotenuse ² = Base² + Altitude ²

10² = 6² + A²

10² - 6² = A²

100 - 36 = A²

64 = A²

8 cm = A

=》The upper end of the ladder touches the wall 8 cm above the ground.

4) AB = Hypotenuse = x

AC = Altitude = 7.2 cm

BC = Base = 2.1 cm

Hypotenuse ² = Base² + Altitude ²

x² = (2.1)² + (7.2)²

x² = 4.41 + 51.84

x² = 56.25

x = √56.25

x = 7.5 cm

=》 Length of AB = 7.5 cm

__________

Hope it helps ⚜