construct a triangle ABC with angleA=60°=angleB and AB=6cm .measure the sides BC and CA. pls help me
Answers
Answer:
Area of rectangle is 192 cm².
Step-by-step explanation:
Given :-
Length of rectangle is 16 cm.
Diagonal of rectangle is 20 cm.
To find :-
Area of rectangle.
Solution :-
First we will find breadth of rectangle because we do not have breadth of rectangle for area.
Let, rectangle be ABCD.
BC be length of rectangle.
AC be diagonal of rectangle.
And, AB be breadth of rectangle.
We know,
All angles of rectangle are of 90°.
So,
∆ABC is a right angle right. ∆ABC will right angled from B.
By Pythagoras theorem :
• Perpendicular² = Hypotenuse² - Base²
Perpendicular = AB
Hypotenuse = AC = 20 cm.
Base = BC = 16 cm.
Put all values in Pythagoras theorem :
⟶ (AB)² = (AC)² + (BC)²
⟶ (AB)² = (20)² + (16)²
⟶ (AB)² = 400 - 256
⟶ (AB)² = 144
⟶ AB = √144
⟶ AB = 12
Thus,
AB is 12 cm.
AB is perpendicular of ∆ABC and AB is breadth of rectangle ABCD.
So, Breadth of rectangle is 12 cm.
We know,
Area of rectangle = Length × Breadth
⟶ Area = 16 × 12
⟶ Area = 192
Therefore,
Area of rectangle is 192 cm².
Answer:
Steps to construct the triangle
Draw a line segment BC=6 cm
At B, draw ∠CBE=60
o
Draw BF⊥BE
Draw the perpendicular bisector of BC intersecting BF at O.
With O as centre and radius equal to OB or OC draw a circle.
With D as centre and radius 5 cm, mark a point A on the circle.
Join AB and AC. This gives △ABC
With B as centre and radius 8 cm, mark an arc which intersect BC produced in C'.
Draw a line parallel to AC at C'.
Extend the line segment BA, which intersect the line passing through C' in A'.
Thus, △A
′
BC
′
is the required triangle.
Here, △A
′
BC
′
∼△ABC [AA similarity]