1.find the perimeter of the rectangle whose length is 40 and diagonal is 41
2.the diagonals of a rhombus measure 16cm and 30cm. find its perimeter
I want answer with steps
Answers
Step-by-step explanation:
1-
As it is mentioned in the question suppose there is a rectangle ABCD and whose length is given 40 cm.
As we know the opposite sides of a rectangle are equal.
If AB = 40 cm that means the side opposite to AB i.e. CD will also be 40 cm.
Now, one of the diagonals of a rectangle is given AC = 41 cm which divides the rectangle into two right-angled triangles.
Now, we can apply the Pythagoras theorem and find the third side that is the breadth of the rectangle.
Let the breadth of the rectangle be AD = x.
Now, in triangle ADC, by Pythagoras theorem (Hypotenuse)2 = (Perpendicular)2 + (Base)2
(AC)2 = (DC)2 + (AD)2
(41)2 = (40)2 + (x)2
1681 = 1600 +(x)2
1681 – 1600 = (x)2
x2 = 81
x = 9 cm
Therefore, breadth of the rectangle = 9 cm
As we know that Perimeter of rectangle = 2(l + b)
= 2(40 + 9)
= 2(49)
= 98 cm
2-
Let PQRS be a rhombus, all sides of rhombus has equal length and its diagonal PR and SQ are intersecting each other at a point O. Diagonals in rhombus bisect each other at 90° .
So, PO = (PR/2)
= 16/2
= 8 cm
And, SO = (SQ/2)
= 30/2
= 15 cm
Then, consider the triangle POS and apply the Pythagoras Theorem,
PS2 = PO2 + SO2
PS2 = 82 + 152
PS2 = 64 + 225
PS2 = 289
PS = √289
PS = 17 cm
Hence, the length of side of rhombus is 17 cm
Now,
Perimeter of Rhombus = 4 × Side of the Rhombus
= 4 × 17
= 68 cm
∴ Perimeter of Rhombus is 68 cm.PS2 = 289
PS = √289
PS = 17 cm
Hence, the length of side of rhombus is 17 cm
Now,
Perimeter of rhombus = 4 × side of the rhombus
= 4 × 17
= 68 cm
∴ Perimeter of rhombus is 68 cm
HOPE IT HELPSS!!
LIKE AND FOLLOW<3
Answer:
1. Perimeter is 98 cm
Step-by-step explanation:
1.Since length is equal to 40 cm and diagonal is equal to 41 cm then by using pythagoras theorem we get the breadth as 9 cm so now by using formula for perimeter we get our answer as 98 cm