Question

A triangle has its longest side as 38 cm If one of the other two sides is 10 cm and the area of the triangle is 152 sq.cm., find the length of the third side O 15/5 cm O 8/97 cm O 15/6 cm O 451 cm​

Answer 1

Answer:

Correct option is

A

1

Giventhat−

ΔABChasAB=20units,BC=10units&arΔABC=80sq.units.

Tofindout−

thelengthofthethirdsideX=AC.

Solution−

WeconstructEuclid

′

sΔABCasdescribedanddrawtheheightoftheΔ

CE=honAB.

LetthethirdsidebeX=AC.

CEwillmeetABatEinternallysinceABisthebiggestside.

SoarΔABC=

2

1

×AB×h⟹h=2×

AB

arΔABC

=2×

20

80

units=8units.

NowCE=h⊥AB.i.eΔBECisarighttriangle.

∴BE=

BC

2

−CE

2

=

10

2

−8

2

units=6units.

i.eAE=AB−BE=(20−6)units=14units.

AgainCE⊥AE.SoΔACEisarighttriangle.

∴X=AC=

AE

2

+CE

2

=

14

2

+8

2

units=

260

units.

Ans−Thethirdside=

260

units.

solution

Expand-image

Answer 2

Answer:

Giventhat−ΔABC has AB=20units,BC=10units&arΔABC=80sq.units.

To find out−the length of the third sideX=AC.

Solution−We construct Euclid′s ΔABC as described and draw the height of the ΔCE=honAB.

Let the thirdside beX=AC.

CE will meet A Bat Einternally

since A Bisthe biggestside.SoarΔABC=21×AB×h⟹h=2×ABarΔABC=2×2080units=8units. NowCE=h⊥AB.i.eΔBECis a right triangle.∴BE=BC2−CE2=10