In triangle ABC, the measure of angle A is 40^\circ and the measure of angle B is 70^\circ… — GRE General Test

In triangle $ABC$ , the measure of angle $A$ is $40^\circ$ and the measure of angle $B$ is $70^\circ$ . If the perimeter of triangle $ABC$ is $22$ centimeters and the length of side $AB$ is $8$ centimeters, what is the length, in centimeters, of side $BC$ ?

A
$4$
$6$ Cevap
C
$7$
D
$8$
E
$14$

Cevap

6 centimeters

First, find the measure of angle

C

180^\circ - 40^\circ - 70^\circ = 70^\circ

. Because angle

B

and angle

C

both measure

70^\circ

, triangle

ABC

is isosceles with sides

AC

and

AB

of equal length (

AC = AB = 8

cm). Since the perimeter is the sum of all three sides (

AB + AC + BC = 22

), substituting the known side lengths gives

8 + 8 + BC = 22

, which yields

BC = 6

cm.

Adım Adım Çözüm

Calculate the measure of the third angle, angle

C

Angle

C = 180^\circ - (40^\circ + 70^\circ) = 70^\circ

The sum of interior angles in any triangle is

180^\circ

Determine the relationship between the side lengths using the angle measures.

Side

AC = AB = 8

centimeters.

Since angle

B = 70^\circ

and angle

C = 70^\circ

, triangle

ABC

is isosceles. Sides opposite equal angles are equal in length, so the side opposite angle

C

(which is

AB

) equals the side opposite angle

B

(which is

AC

Use the perimeter formula to find the length of side

BC

Length of side

BC = 22 - (8 + 8) = 6

centimeters.

Perimeter is the total boundary distance (

AB + AC + BC = 22

). Substituting known values gives

8 + 8 + BC = 22

, so

BC = 6

Anahtar Kavram

Isosceles Triangle Side-Angle Properties and Perimeter

Tahmini Süre:45s

Soru

Cevap

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Anahtar Kavram

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