Question

Explore Activity 2: Yes you Can Do IT!​

Answer 1

`\bold{\huge{\underline{ Solution }}}`

Given :-

• Here, we have given one isosceles trapezoid that is MATH
• In the given trapezoid, MA and HT are the bases and LV is a median
• The length of MA = 3y - 2 , HT = 2y + 4 and LV = 8.5

Part 1 :-

• The value of y = 3

Part 2 :-

Here, we have to

• Find the value of y

We know that the,

Length of the median of trapezium

`\sf{ m = }{\sf{(1)/(2)}}{\sf{ (a + b) }}`

• Here, a and b are the parallel sides of the trapezium.

Subsitute the required values in the above formula :-

`\sf{ LV = }{\sf{(1)/(2)}}{\sf{ [MA + HT]}}`

`\sf{ 8.5 = }{\sf{(1)/(2)}}{\sf{[ (3y - 2) + (2y + 4)]}}`

`\sf{ 8.5 = }{\sf{(1)/(2)}}{\sf{ [3y - 2 + 2y + 4]}}`

`\sf{ 8.5 = }{\sf{(1)/(2)}}{\sf{ [5y + 2] }}`

`\sf{ 8.5 {*}2 = 5y + 3 }`

`\sf{ 17 = 5y + 2 }`

`\sf{ 5y = 17 - 2 }`

`\sf{ 5y = 15 }`

`\bold{ y = 3 }`

Hence, The value of y is 3

Part 3 :-

Here, we have to find the length of MA and HT

• We have, MA = 3y - 2
• HT = 2y + 4

For MA

`\sf{ MA = 3y - 2}`

Subsitute the value of y

`\sf{ MA = 3(3) - 2}`

`\sf{ MA = 9 - 2 }`

`\bold{ MA = 7 }`

For HT

`\sf{ HT = 2y + 4}`

Subsitute the value of y

`\sf{ MA = 2(3) + 4 }`

`\sf{ MA = 6 + 4 }`

`\bold{ MA = 10 }`

Hence, The length of MA and HT are 7 and 10 .