Question

Construct a right triangle when one side is 3.5 cm and the sum of its other side and hypotenuse is 5.5 cm

Answer 1

Construction of right triangle when one side and sum of hypotenuse and the other side is given:

• Draw a line segment AB = 3.5 cm.
• Draw a ray AX from A at 90°.
• Draw an arc on AX with a radius of 5.5 cm.
• Mark this point as C.
• Join BC.
• Measure ACB and draw a ray BY from B such that ∠ACB = ∠CBY and BY passes through AC.
• Mark the point where ray BY meets AC as D.
• ABD is the required triangle.

Answer 2

Sorry friends no geometry tool.

steps of construction:

* Draw a line BC=5.5cm.(base)

*From B, an angle on 90°,Angle XBC

*Cut off BD=5.5cm

*join C to D, CD

*Draw perpendicular bisector AE of line CD, By starting with two points C & D as centres, Draw two arcs on both sides( up & down) with radius approxly a bit more than half of CD.

*The place where this AE bisector intersects BD mark it point A.

*Join A to C, AC.

verification

on measuring by ruler (AB +AC)=5.5cm

Justification

AD=AC .......(1)

(Lies on the same perpendicular bisector AE)

Now: BX=AB+AD=5.5

by equation (1)

BX=AB + AC=5.5

OR

AB+AB=5.5cm

Or

the sum of hypotenuse & one side is 5.5cm,Hence our construction is finished