Answer: ∠ABC = ∠ACB = 45°, AB = BC = 15 units, AC = 20 units.
Step-by-step explanation:
Let the angle with measure 90 degrees be BAC.
∴ AB = BC --------------- Given
∴ ΔABC is an isosceles triangle. -------- (Two sides are equal.)
∴ ∠ABC = ∠ACB ---------- Isosceles Triangle Property. -----------(1)
∴ ∠ABC + ∠ACB + ∠BAC = 180° ------- Sum measures of angles of a triangle
is 180°.
∴ From (1),
∴ ∠ABC + ∠ABC + 90° = 180° ----------- ∠BAC=90° (Given)
∴ 2∠ABC = 180° - 90°
∴ ∠ABC = ∠ACB = [tex]\frac{90}{2}[/tex] = 45°
Now,
AB+BC+AC = 50 ------------ Perimeter of triangle = 50 units (Given)
∴ 3k+3 + 3k+3 + 5k = 50 ----------- Values: Given
∴ 11k+6 = 50
∴ k = [tex]\frac{50-6}{11}[/tex] = [tex]\frac{44}{11}[/tex] = 4
∴ AB = BC = 3k+3 = 3(4) + 3 = 12+3 = 15 units
∴ AC = 5k = 5(4) = 20 units
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Answer: ∠ABC = ∠ACB = 45°, AB = BC = 15 units, AC = 20 units.
Step-by-step explanation:
Let the angle with measure 90 degrees be BAC.
∴ AB = BC --------------- Given
∴ ΔABC is an isosceles triangle. -------- (Two sides are equal.)
∴ ∠ABC = ∠ACB ---------- Isosceles Triangle Property. -----------(1)
∴ ∠ABC + ∠ACB + ∠BAC = 180° ------- Sum measures of angles of a triangle
is 180°.
∴ From (1),
∴ ∠ABC + ∠ABC + 90° = 180° ----------- ∠BAC=90° (Given)
∴ 2∠ABC = 180° - 90°
∴ ∠ABC = ∠ACB = [tex]\frac{90}{2}[/tex] = 45°
Now,
AB+BC+AC = 50 ------------ Perimeter of triangle = 50 units (Given)
∴ 3k+3 + 3k+3 + 5k = 50 ----------- Values: Given
∴ 11k+6 = 50
∴ k = [tex]\frac{50-6}{11}[/tex] = [tex]\frac{44}{11}[/tex] = 4
∴ AB = BC = 3k+3 = 3(4) + 3 = 12+3 = 15 units
∴ AC = 5k = 5(4) = 20 units